The 70 mm width and 146 mm height fit a standard contactor footprint — no surprises for panel layout.
The AC-3 motor rating of 37 kW at 500 V is the headline number — that's the current it can switch under full-load motor starting (inductive load, not resistive). The 690 V rating drops to 18.6 kW because the same contactor has to interrupt a higher voltage with the same arc-quenching capability. If your motor is 400 V, the AC-3 rating is 30 kW (cited as AC-2 at 400 V, 30 kW). The auxiliary contact ratings (2 A at 60 V, 1 A at 110 V, 0.3 A at 220 V) are for the control circuit, not the main power path. The storage range is wider because the contactor isn't switching under load — that's the handling and shelf-life limit, not the running limit.
Solid wire accepts 2x (0.25 to 2.5 mm²) or 2x (2.5 to 16 mm²) depending on the conductor size; stranded accepts 2x (10 to 50 mm²). That covers most panel wiring from control-circuit tails to motor feeders. The pollution degree is 3 (conductive or dry non-conductive pollution), typical for industrial control panels.
If you're comparing it to the 3RT1036-1AB00 (a smaller S2 frame), the 3RT1044-3AG14 is a size up — higher current and power ratings, wider terminals, and a different mounting footprint. It won't drop into a panel wired for the S2 without rewiring the power circuit and possibly the DIN rail bracket.